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I have previously post my question in this topic:

Physics Help and Math Help - Physics Forums > Science Education > Homework & Coursework Questions > Other Sciences > Fick and Cottrell Law

And after Goku suggestion I post my question here.

So my problem deal with the resolution with fick second law of diffusion (in one dimension)

In the case of a planar electrode (one dimension) the current density is proportinnal to the concentration of electroactive species: i=-nFkdC(x=0,t)/dt

From Fick law dC(x,t)/dt=Dd2C(x,t)/d2x

So in the case of initial condition C(x,t=0)=C0

I found this solution (not me, on internet) C(x,t)=C0erf(x/(Dt)1/2)

And so we can deduce Cottrell Law i=-nFAC0(D/Pit)1/2

Now I would like to found the expression of i in the case of spherical electrode and spherical diffusion, wich species are inside the sphere (yes inside and not outside) of radius R

With C(R,t)=0 for t>0 and C(r,t=0)=C0

I would like to found the expression of C(r,t)

I think fick law in spherical diffusion is dC(r,t)/dt=D1/r2d/dr(r2d/dr(C(r,t)))

Is it right?

But now how can I find C(r,t) then dC(r,t)/dr for r=R ???

Do you have any suggestion?

Thank you for your attention

Chris

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# Diffusion equation and fick law

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